Basic Math Examples

${(243^{- \frac{1}{4}})}^{- \frac{4}{5}}$

Step 1

Simplify the expression.

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Step 1.1

Multiply the exponents in ${(243^{- \frac{1}{4}})}^{- \frac{4}{5}}$ .

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Step 1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$243^{- \frac{1}{4} (- \frac{4}{5})}$

Step 1.1.2

Cancel the common factor of $4$ .

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Step 1.1.2.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$243^{\frac{- 1}{4} (- \frac{4}{5})}$

Step 1.1.2.2

Move the leading negative in $- \frac{4}{5}$ into the numerator.

$243^{\frac{- 1}{4} \cdot \frac{- 4}{5}}$

Step 1.1.2.3

Factor $4$ out of $- 4$ .

$243^{\frac{- 1}{4} \cdot \frac{4 (- 1)}{5}}$

Step 1.1.2.4

Cancel the common factor.

$243^{\frac{- 1}{4} \cdot \frac{4 \cdot - 1}{5}}$

Step 1.1.2.5

Rewrite the expression.

$243^{- \frac{- 1}{5}}$

Step 1.1.3

Move the negative in front of the fraction.

$243^{- - \frac{1}{5}}$

Step 1.1.4

Multiply $- - \frac{1}{5}$ .

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Step 1.1.4.1

Multiply $- 1$ by $- 1$ .

$243^{1 (\frac{1}{5})}$

Step 1.1.4.2

Multiply $\frac{1}{5}$ by $1$ .

$243^{\frac{1}{5}}$

Step 1.2

Rewrite $243$ as $3^{5}$ .

${(3^{5})}^{\frac{1}{5}}$

Step 1.3

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$3^{5 (\frac{1}{5})}$

Step 2

Cancel the common factor of $5$ .

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Step 2.1

Cancel the common factor.

$3^{5 (\frac{1}{5})}$

Step 2.2

Rewrite the expression.

$3^{1}$

Step 3

Evaluate the exponent.

$3$